The empirical characteristic function and large sample hypothesis testing

Large Sample Estimation and Hypothesis Testing*

Non-Parametric Testing of Distributions – the Epps-Singleton two-sample test using the Empirical Characteristic Function

In statistics, two-sample tests are used to determine whether two samples have been drawn from the same population. A widely used test as such is the Kolmogorov-Smirnov two-sample test. There are other distribution-free tests which might be applied in similar occasions. In this article, we describe a two-sample omnibus test introduced by Epps and Singleton, which has – albeit being distribution...

Large Sample Estimation and Hypothesis

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Empirical likelihood based hypothesis testing

Omnibus tests for various nonparametric hypotheses are developed using the empirical likelihood method. These include tests for symmetry about zero, changes in distribution, independence and exponentiality. The approach is to localize the empirical likelihood using a suitable ‘time’ variable implicit in the null hypothesis and then form an integral of the log-likelihood ratio statistic. The asy...

Sample Complexity of Testing the Manifold Hypothesis

The hypothesis that high dimensional data tends to lie in the vicinity of a low dimensional manifold is the basis of a collection of methodologies termed Manifold Learning. In this paper, we study statistical aspects of the question of fitting a manifold with a nearly optimal least squared error. Given upper bounds on the dimension, volume, and curvature, we show that Empirical Risk Minimizatio...